Concept explainers
(a)
The force on the cables.

Answer to Problem 13PE
The force in the cables is
Explanation of Solution
Given:
The mass of the bridge is
The mass of the car is
The distance of weight of the bridge from point
The distance of weight of the car from point
The distance of weight of the bridge from point
The length of the bridge is
The angle of force from point
Formula used:
The relation between the weight and the mass of the bridge is
The relation between the weight and the mass of the car is
The relation between the torque and weight of bridge is
The relation between the torque sand weight of car is
The relation between torque of cable is
The relation between the torque of car, bridge and cable is
Figure-(1)
Calculation:
Substituting the given values in equation (1), we get
Substituting the given values in equation (2), we get
Substituting the given values in equation (3), we get
Substituting the given values in equation (4), we get
Substituting the given values in equation (5), we get
Substituting the given values in equation (6), we get
Conclusion:
Thus, the force in the cables is
(b)
The direction and magnitude of force exerted by the hinges on the bridge.

Answer to Problem 13PE
The magnitude of force exerted by the hinges on the bridge is
Explanation of Solution
Formula used:
The relation between force in the horizontal direction and torque is
The relation between force in the vertical direction and torque is
The relation between the force and vertical and horizontal forces is
The relation between the angle made by force and vertical and horizontal forces is
Calculation:
Substituting the given values in equation (7), we get
Substituting the given values in equation (8), we get
Substituting the given values in equation (9), we get
Substituting the given values in equation (10), we get
Conclusion:
Thus, the magnitude of force exerted by the hinges on the bridge is
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Chapter 9 Solutions
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